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GIFT  OF 
Prof*   R.   Tracy  Crawford 


^.S^Is/i.-^t.'^^y^^J^- 


FOUR-PLACE  i'{ 
LOGARITHMS 


BY 

GEORGE  William/ JONES 

Professor   of    Mathematics    in    Cornell    University 


I.     Four-place  Logarithms  of  Three-figure 

XUMBERS. 

II.  The  Natural  Sines,  Cosikes,  Tangents, 
AND  Cotangents  of  Angles  differing 
BY  Ten  Minutes,  and  their  Four- 
place  Logarithms. 


A  good  collection  of  Mathematical  Tables  is  like  a 
Dictionary :  it  may  lie  on  the  shelf  for  months, 
hut  ichen  it  is  loanted  it  is  ivanted,  and  its  use  for 
a  single  hour  may  he  ivorth  the  iwice  of  the  hook. 


JONES'    FIVE-PLACE    LOGARITHMS. 

PAGES 
I.    LOGARITHMS  OF  NUMBERS,       ...  -       2-19 

A  table  of  five-place  logarithms  of  four-figure  num- 
bers, with  differences  for  a  fifth  figure. 

II.    TRIGONOMETRIC  FUNCTIONS,  ...  -      20-64 

A  table  of  natural  sines,  cosines,  tangents  and  co- 
tangents of  angles  0°-180°,  to  minutes,  and  of  their 
five-place  logarithms,  with  differences  for  seconds. 

III.    MINOR  TABLES,  -.         -  .  .  -  -       3-19 

Natural  Logarithms;  Ten.Place  Logarithms;  Weights 
and  Measures;  Mathematical  Constants;  Mei-idionai 
Parts;  Square.Roots;  Cube-Roots;  Reciprocals;  Sines 
and  Tangents  of  Small  Angles. 


JONES'   LOGARITHMIC  TABLES. 

FOUR-PLACE,  SIX-PLACE,  AND   TEN-PLACE. 

EXPLANATION  OF  THE  TABLES,  ....  3-11 

I.    FOUR-PLACE  LOGARITHMS,  -  -  .  12-14 

A  four-place  table  of  logarithms  of  the  natural  num- 
bers 1,  2,  3,.. 999,  with  a  table  of  proportional  differ- 
ences in  the  margin,  and  of  the  logarithms  of  the 
squares,  cubes,  squai-e-roots,  cube-roots  and  recip- 
rocals  of  the  numbers  1,  3,  3,. ,99. 

IL    FOUR-PLACE  TRIGONOMETRIC  FUNCTIONS,        -       15-19 
A  four-place  table  of  logarithms  of  the  six  principal 
trigonometric  functions,  Avith  differences  for  min- 
utes, and  of  the  length  of  arcs  in  radians. 

III.  LOGARITHMS  OF  NUMBERS,  -  -  -  20-37 

A  six-place  table  of  logarithms  of  four-figure  num- 
bers, with  a  table  of  differences. 

IV.  CONSTANTS  OF  MATHEMATICS  AND  OF  NATURE 

—WEIGHTS  AND  MEASURES,  -  -  38-41 

A  table  of  useful  constants,  with  the  logarithms  of 
those  in  common  use. 

V.    ADDITION-SUBTRACTION  LOGARITHMS,  .  43-58 

A  six-place  table  of  logarithms  so  i-elated  that,  by 
their  use,  the  logarithm  of  the  sum  and  of  the  diff. 
erence  of  two  numbers  may  be  found  from  their 
logarithms  without  taking  o\xt  the  numbers  them- 
selves. 

VL    SINES  AND  TANGENTS  OF  SMALL  ANGLES,     -  59 

A  table  of  the  ratios  sinA":A,  tanA":A  for  angles 
0°-5°,  whereby  the  logarithmic  sines  and  tangents  of 
these  small  angles  are  found  more  exactly  than  by 
Table  VII. 

(SEE  THE  THIRD   COVER   PAGE.) 


FOUK-PLACE    LOGAEITHMS.  -i  ^r^ 

FORM   OF  A  LOGARITHM.  ^r^Ji.J(r^ 

The  Logarithm  of  a  number  is  the  exponent  of  that  power  to  which  another  number, 
the  base,  must  be  raised  to  give  tlie  number  first  named.  The  base  commonly  used  is  10  ; 
and  as  most  numbers  are  incommensurable  powers  of  10,  a  common  logarithm,  in  general, 
consists  of  an  integer,  the  charactenstic,  and  an  endless  decimal,  the  mantissa. 

If  a  number  be  resolved  into  two  .factors,  of  which  one  is  an  integer  power  of  10  and  the 
other  lies  between  1  and  10,  then  the  exponent  of  10  is  the  characteristic,  and  the  logarithm 
of  the  other  factor  is  the  mantissa.  The  characteristic  is- positive  if  the  number  be  larger 
than  1 ,  and  negative  if  it  be  smaller  ;  the  mantissa  is  always  positive.  A  negative  character- 
istic is  indicated  by  the  sign  —  above  it.  The  logarithms  of  numbers  that  differ  only  by 
the  position  of  the  decimal  point  have  different  characteristics  but  the  same  mantissa. 
J&.5'.  7770  =  103x7.77  and  log  7770  =  3.8904  ;  .0777  =  10-2x7.77,  and  log  .0777  =  2.8904. 
tables  of  logarithms. 

The  logarithms  of  any  set  of  consecutive  numbers,  arranged  in  a  form  convenient  for 
use,  constitute  a  table  of  logarithms.  Such  a  table  to  the  base  10  need  give  only  the  man- 
tissas ;  the  characteristics  are  manifest.  This  table  is  arranged  upon  the  common  double- 
entry  plan  i.e.  the  mantissa  of  the  logarithm  of  a  three-figure  number  stands  opposite  the 
first  two  figures  and  under  the  third  figure.  The  logarithms  are  given  correct  to  four  places. 
to  take  out  the  logarithm  of  a  number. 

A  three-figure  number :  Take  out  the  tabular  mantissa  that  lies  in  line  with  the  first  two 
figures  of  the  number  and  under  the  third  figure  ;  the  characteristic  is  the  exponent  of  that 
integer  power  of  10  which  lies  next  below  the  number. 
E.g.  log  677  =  2.8306,    log  6.78  =  0.8312,    log  .0679  =  2.8319,    log  676  000  =  5.8299. 

A  number  of  less  than  three  figures :  Make  the  number  a  three-figure  number  by  annex- 
ing zeros,  and  follow  the  rale  given  above. 

^.g-.  log  700  =  2.8451,    log  7  =  0.8451,    log  .0071  =  3.a513,    log  71  000  =  4.8513. 

A  four  figure  number :  Take  out  the  tabular  mantissa  of  the  first  three  figures,  and  add 
such  part  of  the  difference  between  this  mantissa  and  the  next  greater  tabular  mantissa 
(the  tabular  difference).,  as  the  fourth  figure  is  a  part  of  10  ;  and  so  for  a  five-figure  number. 
^.^.  •.•log678     =2.8312     and     log  679  =  2.8319, 

.'.  log  678.6  =  2.8312 +  .0007  x  6/10  =  2.8316,   log  6.7875=0.8312  +  .0007  x  75/100=0.8317. 

TO  TAKE   OUT  A  NUMBER  FROM   ITS  LOGARITHM. 

The  mantissa  found  in  the  table .-  Join  the  figure  at  the  top  that  lies  above  the  given 
mantissa  to  the  two  figures  upon  the  same  line  at  the  extreme  left  ;  in  this  three-figure 
number  so  place  the  decimal  point  that  the  number  shall  be  next  above  that  power  of  10 
whose  exponent  is  the  characteristic  of  the  logarithm. 
JE-.j/.  log-i  2.8312  =  678,    log-i  0.8451  =  7,    log-i  3.8513  =  .0071,    log-1  5.8513  =  710000. 

The  mantissa  not  found  in  the  table ,-  Take  out  the  three-figure  number  of  the  tabular 
mantissa  next  less  than  the  given  mantissa,  and  to  these  three  figures  join  the  quotient  of 
the  difference  of  these  two  mantissas  by  the  tabular  difference. 
E.g.  •.-  log  678  =  2.8312    and    log  679  =  2.8319, 

.-.  log-i  2.8316  =  678J  =  678.6,    log-i  2.8317  =  .0678f  =  .06787. 


The  use  of  trigonometric  ratios  and  their  logarithms  is  explained  in  works  on  trigonometry. 


1 

0 

1 

2 

3 

4 

5 

6 

h 
i 

8 

9 

0 

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0000 

3010 

4771 

6021 

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4 

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5 

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12 

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0828 

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1004 

1038 

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1106 

13 

1139 

1173 

1206 

1239 

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1303 

1335 

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1430 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

225  3 

2279 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

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2529 

18 

2553 

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2601 

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2648 

2672 

2695 

2718 

2742 

2765 

19 

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2810 

2833 

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2878 

2900 

2923 

2945 

2967 

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20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

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31 

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3243 

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3324 

3345 

3365 

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22 

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3522 

3541 

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23 

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27 

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29 

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4683 

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4713 

4728 

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30 

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4786 

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31 

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4928 

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5024 

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5065 

5079 

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5105 

5119 

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5145 

5159 

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33 

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5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

34 

5315 

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5340 

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5366 

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5391 

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5416 

5428 

35 

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5465 

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5502 

5514 

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36 

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5611 

5623 

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5763 

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41 

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49 

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6911 

6920 

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6937 

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50 

0 

1 

2 

3 

4 

5 

6 

7 

8 

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1 

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0 

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3 

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7007 

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7118 

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52 

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53 

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57 

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63 

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8000 

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65 

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66 

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8228 

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8248 

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67 

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69 

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87 

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89 

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90 

9542 

9547 

9552 

9557 

9562 

9566 

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91 

9590 

9595 

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9605 

9609 

9614 

9619 

9624 

9628 

9638 

92 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

100 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

ANGLE. 

SINES. 

COSINES. 

TANGENTS.     COTANGENTS. 

ANGLE. 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

0°00' 

.0000   00 

1.0000  0.0000 

.0000    00     00 

00 

90°00' 

10 

.0029  7.4637 

1.0000   0000 

.0029  7.4637  2.5363 

343.77 

50 

20 

.0058   7648 

1.0000   0000 

.0058   7648   2352 

171.89 

40 

30 

.0087   9408 

1.0000   0000 

.0087   9409   0591 

114,59 

30 

40 

.0116  8.0658 

.9999   0000 

.0116  8.0658  1.9342 

85.940 

20 

50 

.0145   1627 

.9999   0000 

.0145   1627   8373 

68,750 

10 

1°00' 

.0175  8.2419 

.9998  9.9999 

.0175  8.2419  1.7581 

57.290 

89°00' 

10 

.0204   3088 

.9998   9999 

.0204   3089   6911 

49.104 

50 

20 

.0233   3668 

.9997   9999 

.0233   3669   6331 

42.964 

40 

30 

.0262   4179 

.9997   9999 

.0262   4181   5819 

38.188 

30 

40 

.0291   4637 

.9996   9998 

.0291   4638   5362 

34.368 

20 

50 

.0320   5050 

.9995   9998 

.0320   5053   4947 

31.242 

10 

2°00' 

.0349  8.5428 

.9994  9.9997 

.0349  8.5431  1.4569 

28.636 

88°00' 

10 

.0378   5776 

.9993   9997 

.0378   5779   4221 

26.432 

50 

20 

.0407   6097 

.9992   9996 

.0407   6101   3899 

24.542 

40 

30 

.0436   6397 

.9990   9996 

.0437   6401   3599 

22.904 

30 

40 

.0465   6677 

.9989   9995 

.0466   6682   3318 

21.470 

20 

50 

.0494   6940 

.9988   9995 

.0495   6945   3055 

20.206 

10 

3°00' 

.0523  8.7188 

.9986  9.9994 

.0524  8.7194  1.2806 

19.081 

87°00' 

10 

.0552   7423 

.9985   9993 

.0553   7429   2571 

18.075 

50 

20 

.0581   7645 

.9983   9993 

.0582   7652   2348 

17.169 

40 

30 

.0610   7857 

.9981   9992 

.0612   7865   2135 

16.350 

30 

40 

.0640   8059 

.9980   9991 

.0641   8067   1933 

15.605 

20 

50 

.0669   8251 

.9978   9990 

.0670   8261   1739 

14.924 

10 

4°00' 

.0698  8.8436 

.9976  9.9989 

.0699  8.8446  1.1554 

14.301 

86°00' 

10 

.0727   8613 

.9974   9989 

.0729   8624   1376 

13.727 

50 

20 

.0756   8783 

.9971   9988 

.0758   8795   1205 

13.197 

40 

30 

.0785   8946 

.9969   9987 

.0787   8960   1040 

12.706 

30 

40 

.0814   9104 

.9967   9986 

.0816   9118   0882 

12.251 

20 

50 

.0843   9256 

.9964   9985 

.0846   9272   0728 

11.826 

10 

50OO' 

.0872  8.9403 

.9962  9.9983 

.0875  8.9420  1.0580 

11.430 

85°00' 

10 

.0901   9545 

.9959   9982 

.0904   9563   0437 

11.059 

50 

20 

.0929   9682 

.9957   9981 

,0934   9701   0299 

10.712 

40 

30 

.0958   9816 

.9954   9980 

,0963   9836   0164 

10.385 

30 

40 

.0987   9945 

.9951   9979 

.0992   9966   0034 

10.078 

20 

50 

.1016  9.0070 

.9948   9977 

,1022  9.0093  0.9907 

9.7882 

10 

6  =  00' 

.1045  9.0192 

.9945  9.9976 

,1051  9.0216  0.9784 

9.5144 

84°00' 

10 

.1074   0311 

.9942   9975 

.1080   0336   9664 

9.2553 

50 

20 

.1103   0426 

.9939   9973 

.1110   0453   9547 

9.0098 

40 

30 

.1132   0539 

.9936   9972 

.1139   0567   9433 

8.7769 

30 

40 

.1161   0648 

.9932   9971 

.1169   0678   9322 

8.5555 

20 

50 

.1190   0755 

,9929   9969 

.1198   0786   9214 

8.3450 

10 

r°oo' 

.1219  9.0859 

.9925  9.9968 

.1228  9.0891  0.9109 

8.1443 

83000' 

10 

.1248   0961 

.9922   9966 

.1257   0995   9005 

7.9530 

50 

20 

.1276   1060 

.9918   9964 

.1287   1096   8904 

7.7704 

40 

30 

.1305   1157 

.9914   9963 

.1317   1194   8806 

7.5958 

30 

40 

.1334   1252 

.9911   9961 

,1346   1291   8709 

7.4287 

20 

50 

.1363   1345 

.9907   9959 

.1376   1385   8615 

7.2687 

10 

8°00' 

.1392  9.1436 

.9903  9.9958 

.1405  9.1478  0.8522 

7.1154 

82°00' 

10 

.1421   1525 

.9899   9956 

.1435   1569   8431 

6.9682 

50 

20 

.1449   1612 

.9894   9954 

.1465   1658   8342 

6.8269 

40 

30 

.1478   1697 

.9890   9952 

.1495   1745   8255 

6.6912 

30 

40 

.1507   1781 

.9886   9950 

.1524   1831   8169 

6.5606 

20 

50 

.1536   1863 

.9881   9948 

.1554   1915   8085 

6.4348 

10 

9°00' 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997  0.8003 

6.3138 

81°00' 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

ANGLE. 

COSINES. 

SINES. 

COTANGENTS.      TANGENTS. 

ANGLE. 

ANGLE. 

SINES. 

COSINES. 

TANGENTS.      COTANGENTS. 

ANGLE. 

Nat.  Log. 

Nat,  Log. 

Nat.   Log.   Log. 

Nat. 

9»00' 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997  0.8003 

6.3138 

81°00' 

10 

.1593   2022 

.9872   9944 

.1614   2078   7922 

6.1970 

50 

20 

.1622   2100 

.9868   9942 

.1644   2158   7842 

6.0844 

40 

30 

.1650   2176 

.9863   9940 

.1673   2236   7764 

5.9758 

30 

40 

.1679   2251 

.9858   9938 

.1703   2313   7687 

5.8708 

20 

50 

.1708   2324 

.9853  9936 

.1733   2389   7611 

5.7694 

10 

WOO' 

.1736  9.2397 

.9848  9.9934 

.1763  9.2463  0.7537 

5.6713 

80°00' 

10 

.1765   2468 

.9843   9931 

.1793   2536   7464 

5.5764 

50 

20 

.1794   2538 

.9838   9929 

.1823   2609   7391 

5.4845 

40 

30 

.1822   2606 

.9833  •  9927 

.1853   2680   7320 

5.3955 

30 

40 

.1851   2674 

.9827   9924 

.1883   2750   7250 

5.3093 

20 

50 

.1880   2740 

.9822   9922 

.1914   2819   7181 

5.2257 

10 

11°00' 

.1908  9.2806 

.9816  9.9919 

.1944  9.2887  0.7113 

5.1446 

79°00' 

10 

.1937   2870 

.9811   9917 

.1974   2953   7047 

5.0658 

50 

20 

.1965   2934 

.9805   9914 

.2004   3020   6980 

4.9894 

40 

30 

.1994   2997 

.9799   9912 

.2035   3085   6915 

4.9152 

30 

40 

.2022   3058 

.9793   9909 

.2065   3149   6851 

4.8430 

20 

50 

.2051   3119 

.9787   9907 

.2095   3212   6788 

4.7729 

10 

12°00' 

.2079  9.3179 

.9781  9.9904 

.2126  9,3275  0.6725 

4.7046 

78°00' 

10 

.2108   3238 

.9775   9901 

.2156   3336   6664 

4.6382 

50 

20 

.2136   3296 

.9769   9899 

.2186   3397   6003 

4.5736 

40 

30 

.2164   3353 

.9763   9896 

.2217   3458   6542 

4.5107 

30 

40 

.2193   3410 

.9757   9893 

.2247   3517   6483 

4.4494 

20 

50 

.2221   3466 

.9750   9890 

.2278   3576   6424 

4.3897 

10 

IS'OO' 

.2250  9.3521 

.9744  9.9887 

.2309  9.3634  0.6366 

4.3315 

77°00' 

'10 

.2278   3575 

.9737   9884 

.2339   3691   6309 

4.2747 

50 

20 

.2300   3629 

.9730   9881 

.2370   3748   6252 

4.2193 

40 

30 

.2334   3682 

.9724   9878 

.2401   3804   6196 

4.1653 

30 

40 

.2363   3734 

.9717   9875 

.2432   3859   6141 

4.112  6 

20 

50 

.2391   3786 

.9710   9872 

.2462   3914   6086 

4.0611 

10 

14000' 

.2419  9.3837 

.9703  9.9869 

.2493  9.3968  0.6032 

4.0108 

76°00/ 

10 

.2447   3887 

.9696   9866 

.2524   4021   5979 

3.9617 

50 

20 

.2476   3937 

.9689   9863 

.2555   4074   5926 

3.9136 

40 

30 

.2504   3986 

.9681   9859 

.2586   4127   5873 

3.8667 

30 

40 

.2532   4035 

.9674   9856 

.2617   4178   5822 

3.8208 

20 

50 

.2560   4083 

.0667   9853 

.2648   4230   5770 

3.7760 

10 

15°00' 

.2588  9.4130 

.9659  9.9849 

.2679  9.4281  0.5719 

3.7321 

75°00' 

10 

.2616   4177 

.9653   9846 

.2711   4331   5669 

3.6891 

50 

^         20 

.2644   4223 

.9644   9843 

.2742   4381   5619 

3.6470 

40 

30 

.2672   4269 

.9036   9839 

.2773   4430   5570 

3.6059 

30 

40 

.2700   4314 

.9628   9836 

.8805   4479   5521 

3.5656 

20 

50 

.2728   4359 

.9621   9832 

.2836   4527   5473 

3.5261 

10 

16000' 

.2756  9.4403 

.9613  9.9828 

.2867  9.4575  0.5425 

3.4874 

74°00' 

10 

.2784   4447 

.9605   9825 

.2899   4622   5378 

3.4495 

50 

20 

.2818   4491 

.9596   9821 

.2931   4669   5331 

3.4124 

40 

30 

.2840   4533 

.9588   9817 

.2962   4716   5284 

3.3759 

30 

40 

.2868   4576 

.9580   9814 

.2994   4762   5238 

3.3402 

20 

50 

.2896   4618 

.9572   9810 

.3026   4808   5192 

3.3052 

10 

I70OO' 

.2924  9.4659 

.9563  9.9806 

.3057  9.4853  0.5147 

3.2709 

730OO' 

10 

.2952   4700 

.9555   9802 

.3089   4898   5102 

3.2371 

50 

20 

.2979   4741 

.9546   9798 

.3121   4943   5057 

3.2041 

40 

30 

.3007   4781 

.9537   9794 

.3153   4987   5013 

3.1716 

30 

40 

.3035   4821 

.9528   9790 

.3185   5031   4969 

3.1397 

20 

50 

.3062   4861 

.9520   9786 

.3217   5075   4925 

3.1084 

10 

18°00' 

.3090  9.4900 

.9611  9.9782 

.3249  9.5118  0.4882 

3.0777 

72O00' 

Nat.  Log. 

Nat.  Log. 

Nat.   Log.   Log. 

Nat. 

SENTS. 

ANGLE. 

COSINES. 

SINES. 

COTANGENTS.      TAN 

ANGLE. 

ANGLE. 

SINES. 

COSINES. 

TANGENTS.      COTANGENTS. 

ANGLE. 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

18°00' 

.3090  9.4900 

.9511  9.9782 

.3249  9.5118  0.4882 

3.0777 

72°00' 

10 

.3118   4939 

.9502   9778 

.3281   5J61   4839 

3.0475 

50 

20 

.3145   4977 

.9492   9774 

.3314   5203   4797 

3.0178 

40 

30 

.3173   5015 

.9483   9770 

.3346   5245   4755 

2.9887 

30 

40 

.3201   5052 

.9474   9765 

.3378   5287   4713 

2.9600 

20 

50 

.3228   5090 

.9465   9761 

.3411   5329   4671 

2.9319 

10 

19°00' 

.3256  9.5126 

.9455  9.9757 

.3443  9.5370  0.4630 

2.9042 

71°00' 

10 

.3283   5163 

.9446   9752 

.3476   5411   4589 

2.8770 

50 

20 

.3311   5199 

.9436   9748 

.3508   5451   4549 

2.8502 

40 

30 

.3338   5235 

.9426   9743 

.3541   5491   4509 

2.8239 

30 

40 

.3365   5270 

.9417   9739 

.3574   5531   4469 

2.7980 

20 

50 

.3393   5306 

.9407   9734 

.3607   5571   4429 

2.7725 

10 

20000' 

•3420  9.5341 

.9397  9.9730 

.3640  9.5611  0.4389 

2.7475 

70°00' 

10 

.3448   5375 

.9387   9725 

.3673   5650   4350 

2.7228 

50 

20 

.3475   5409 

.9377   9721 

.3706   5689   4311 

2.6985 

40 

30 

.3502   5443 

.9367   9716 

.3739   5727   4273 

2.6746 

30 

40 

.3529   5477 

.9356   9711 

.3772   5766   4234 

2.6511 

20 

50 

.3557   5510 

.9346   9706 

.3805   5804   4196 

2.6279 

10 

21°00' 

.3584  9.5543 

.9336  9.9702 

.3839  9.5842  0.4158 

2.6051 

69°00' 

10 

.3611   5576 

.9325   9697 

.3872   5879   4121 

2.5826 

50 

20 

.3638   5609 

.9315   9692 

.3906   5917   4083 

2.5605 

40 

30 

.3665   5641 

.9304   9687 

.3939   5954   4046 

2.5386 

30 

40 

.3692   5673 

.9293   9682 

.3973   5991   4009 

2.5172 

20 

50 

.3719   5704 

.9283   9677 

.4006   6028   3972 

2.4960 

10 

22°00' 

.3746  9.5736 

.9272  9.9672 

.4040  9.6064  0.3936 

2.4751 

68°00' 

10 

.3773   5767 

.9261   9667 

.4074   6100   3900 

2.4545 

50 

20 

.3800   5798 

.9250   9661 

.4108   6136   3864 

2.4342 

40 

3  0 

.3827   5828 

.9239   9656 

.4142   6172   3828 

2.4142 

30 

40 

.3854   5859 

.9228   9651 

.4176   6208   3792 

2.3945 

20 

50 

.3881   5889 

.9216   9646 

.4210   6243   3757 

2.3750 

10 

23»00' 

.3907  9.5919 

.9205  9.9640 

.4245  9.6279  0.3721 

2.3559 

67°00' 

10 

.3934   5948 

.9194   9635 

.4279   6314   3686 

2.3369 

50 

20 

.3961   5978 

.9182   9629 

.4314   6348   3652 

2.3183 

40 

30 

.3987   6007 

.9171   9624 

.4348   6383   3617 

2.2998 

30 

40 

.4014   6036 

.9159   9618 

.4383   6417   3583 

2.2817 

20 

50 

.4041   6065 

.9147   9613 

.4417   6452   3548 

2.2637 

10 

24°00' 

.4067  9.6093 

.9135  9.9607 

.4452  9.6486  0.3514 

2.2460 

66°00' 

10 

.4094   6121 

.9124   9602 

.4487   6520   3480 

2.2286 

50 

20 

.4120   6149 

.9112   9596 

.4522   6553   3447 

2.2113 

40 

30 

.4147   6177 

.9100   9590 

.4557   6587   3413 

2.1943 

30 

40 

.4173   6205 

.9088   9584 

.4592   6620   3380 

2.1775 

20 

50 

.4200   6232 

.9075   9579 

.4628   6654   3346 

2.1609 

10 

25°00' 

.4226  9.6259 

.9063  9.9573 

.4663  9.6687  0.3313 

2.1445 

65°00' 

10 

.4253   6286 

.9051   9567 

.4699   6720   3280 

2.1283 

50 

20 

.4279   6313 

.9038   9561 

.4734   6752   3248 

2.1123 

40 

30 

.4305   6340 

.9026   9555 

.4770   6785   3215 

2.0965 

30 

40 

.4331   6366 

.9013   9549 

.4806   6817   3183 

2.0809 

20 

50 

.4358   6392 

,9001   9543 

.4841   6850   3150 

2.0655 

10 

26«00' 

.4384  9.6418 

.8988  9.9537 

.4877  9.6882  0.3118 

2.0503 

64°00' 

10 

.4410   6444 

.8975   9530 

.4913   6914   3086 

2.0353 

50 

20 

.4436   6470 

.8962   9524 

.4950   6946   3054 

2.0204 

40 

30 

.4462   6495 

.8949   9518 

.4986   6977   3023 

2.0057 

30 

40 

.4488   6521 

.8936   9512 

.5022   7009   2991 

1.9912 

20 

50 

.4514   6546 

.8923   9505 

.5059   7040   2960 

1.9768 

10 

27»00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072  0.2928 

1.9626 

63°00' 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

JENTS. 

ANGLE. 

COSINES. 

SINES. 

COTANGENTS.     TANC 

ANGLE. 

ANGLE. 

SINE9. 

COSINES. 

TANGENTS.     COTANGENTS. 

ANGLE. 

Nat.   Log. 

Nat.  Log. 

Nat.   Log,   Log. 

Nat. 

27»00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072  0.2928 

1.9626 

63*00' 

10 

.4566   6595 

.8897   9492 

.5132  7103  2897 

1.9486 

50 

20 

.4592   6620 

.8884   9486 

.5169   7134   2866 

1.9347 

40 

30 

.4617   6644 

.8870   9479 

.5206   7165   2835 

1.9210 

30 

40 

.4643   6668 

.8857  9473 

.5243   7196   2804 

1.9074 

20 

50 

.4669   6692 

.8843  9466 

.5280   7226   2774 

1.8940 

10 

28»00' 

.4695  9.6716 

.8829  9.9459 

.5317  9.7257  0.2743 

1.8807 

62°00' 

10 

.4720   6740 

.8816   9453 

.5354   7287   2713 

1.8676 

50 

20 

.4746   6763 

.8802  9446 

.5392   7317   2683 

1.8546 

40 

30 

.4772   6787 

.8788  9439 

.5430   7348   2652 

1.8418 

30 

40 

.4797   6810 

.8774  9432 

.5467   7378   2622 

1.8291 

20 

50 

.4833  6833 

.8760   9425 

.5505   7408   2592 

1.8165 

10 

29°00' 

.4848  9.6856 

.8746  9.9418 

.5543  9.7438  0.2562 

1.8040 

61*00' 

10 

.4874   6878 

.8732   9411 

.5581   7467   2533 

1.7917 

50 

20 

.4899   6901 

.8718   9404 

.5619   7497   2503 

1.7796 

40 

30 

.4924   6923 

.8704   9397 

.5658   7526   2474 

1.7675 

30 

40 

.4950   6946 

.8689   9390 

.5696   7556   2444 

1.7556 

20 

50 

.4975   6968 

.8675  9383 

.5735   7585   2415 

1.7437 

10 

30«00' 

.5000  9.6990 

.8660  9.9375 

.5774  9.7614  0.2386 

1.7321 

60*00' 

10 

.5025   7012 

.8646   9368 

.5812   7644   2356 

1.7205 

50 

20 

.5050   7033 

.8631   9361 

.5851   7673   2327 

1.7090 

40 

30 

.5075   7055 

.8616   9353 

.5890   7701   2299 

1.6977 

30 

40 

.5100   7076 

.8601   9346 

.5930   7730   2270 

1.6884 

20 

50 

.5125   7097 

.8587  9338 

.5969   7759   2241 

1.6753 

10 

31000' 

.5150  9.7118 

.8572  9.9331 

.6009  9.7788  0.2212 

1.6643 

59°00' 

10 

.5175   7139 

.8557   9323 

.6048   7816   2184 

1.6534 

50 

20 

.5200   7160 

.8542   9315 

.6088   7845   2155 

1.6426 

40 

30 

.5225   7181 

.8526   9308 

.6128  7873  2127 

1.6319 

30 

40 

.5250   7201 

.8511   9300 

.6168   7902   2098 

1.6212 

20 

50 

.5275   7222 

.8496   9292 

.6208  7930  2070 

1.6107 

.  10 

32»00' 

.5299  9.7242 

.8480  9.9284 

.6249  9.7958  0.2042 

1.6003 

58»00' 

10 

.5324   7262 

.8465   9276 

.6289   7986   2014 

1.5900 

50 

20 

.5348   7282 

.8450   9268 

.6330   8014   1986 

1.5798 

40 

30 

.5373   7302 

.8434   9260 

.6371   8042   1958 

1.5697 

30 

40 

.5398   7322 

.8418   9252 

.6412   8070   1930 

1.5597 

20 

50 

.5423   7342 

.8403   9244 

.6453   8097   1903 

1.5497 

10 

33°00' 

.5446  9.7361 

.8387  9.9236 

.6494  9.8125  0.1875 

1.5399 

57*00' 

10 

.5471   7380 

.8371   9228 

.6536   8153   1847 

1.5301 

50 

20 

.5495   7400 

.8355   9219 

.6577   8180   1820 

1.5204 

40 

30 

.5519   7419 

.8339   9211 

.6619   8208   1792 

1.5108 

30 

40 

.5544   7438 

.8323   9203 

.6661   8235   1765 

1.5013 

20 

50 

.5568   7457 

.8307   9194 

.6703   8263   1737 

1.4919 

10 

34°00' 

.5592  9.7476 

.8290  9.9186 

.6745  9.8290  0.1710 

1.4826 

56*00' 

10 

.5616   7494 

.8274   9177 

.6787  8317  1683 

1.4733 

50 

20 

.5640   7513 

.8258   9169 

.6830   8344   1656 

1.4641 

40 

30 

.5664   7531 

.8241   9160 

.6873   8371   1629 

1.4550 

30 

40 

.5688   7550 

.8225   9151 

.6916   8398   1602 

1.4460 

20 

50 

.5712   7568 

.8208   9142 

.6959   8425   1575 

1.4370 

10 

35»00' 

.5736  9.7586 

.8192  9.9134 

.7002  9.8452  0.1548 

1.4281 

55*00' 

10 

.5760   7604 

.8175   9125 

.7046   8479   1521 

1.4193 

50 

20 

.5783   7622 

.8158   9116 

.7089   8506   1494 

1.4106 

40 

30 

.5807   7640 

.8141   9107 

.7133  8533   1467 

1.4019 

30 

40 

.5831   7657 

.8124   9098 

.7177   8559   1441 

1.3934 

20 

50 

.5854   7675 

.8107   9089 

.7221   8586   1414 

1.3848 

10 

36°00' 

.5873  9.7692 

.8090  9.9080 

.7265  9.8613  0.1387 

1.3764 

54*00' 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

GENTS. 

ANGLE. 

COSINES. 

SINES. 

COTANGENTS.     TAN 

ANGLE. 

ANGLE. 

SINES. 

COSINES. 

TANGENTS.      COTANGENTS. 

ANGLE. 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

36°00' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613  0.1387 

1.3764 

54°00' 

10 

.5901   7710 

.8073   9070 

.7310   8639   1361 

1.3680 

50 

20 

.5925   7727 

.8056   9061 

.7355   8666   1334 

1.3597 

40 

30 

.5948   7744 

.8039   9052 

.7400   8692   1308 

1.3514 

30 

40 

.5972   7761 

.8021   9042 

.7445   8718   1282 

1.3432 

20 

50 

.5995   7778 

.8004   9033 

.7490   8745   1255 

1.3351 

10 

37°00' 

.6018  9.7795 

.7986  9.9023 

.7536  9.8771  0.1229 

1.3270 

53°00' 

10 

.6041   7811 

.7969   9014 

.7581   8797   1203 

1.3190 

50 

20 

.6065   7828 

.7951   9004 

.7627   8824   1176 

1.3111 

40 

30 

.6088   7844 

.7934   8995 

.7673   8850   1150 

1.3032 

30 

40 

.6111   7861 

.79-16   8985 

.7720   8876   1124 

1.2954 

20 

50 

.6134  7877 

.7898   8975 

.7766   8902   1098 

1.2876 

10 

38=00' 

.6157  9.7893 

.7880  9.8965 

.7813  9.8928  0.1072 

1.2799 

52°00' 

10  • 

.6180   7910 

.7862   8955 

.7860   8954   1046 

1.2723 

50 

20 

.6202   79,26 

.7844  S^ib 

.7907   8980   1020 

1.2647 

40 

30 

.6225   7941 

.7826   8935 

.7954   9006   0994 

1.2572 

30 

40 

.6248   7957 

.7808   8925 

.8002   9  32   0968 

1.2497 

20 

50 

.6271   7973 

.7790   8915 

.8050   9058  0942 

1.2423 

10 

39°00' 

.6293  9.7989 

.7771  9.8905 

.8098  9.9084  0.0916 

1.2349 

51°00' 

10 

.6316   8004 

.7753   8895 

.8146   9110   0890 

1.2276 

50 

20 

.6338   8020 

.7735   8884 

.8195   9135   0865 

1.2203 

40 

30 

.6361   8035 

.7716   8874 

.8243   9161   0839 

1.2131 

30 

40 

.6383   8050 

.7698   8864 

.8292   9187   0813 

1.2059 

20 

50 

.6406   8066 

.7679   8853 

.8342   9212   0788 

1.1988 

10 

40°00' 

.6428  9.8081 

.7660  9.8843 

.8391  9.9238  0.0762 

1.1918 

50°00' 

10 

.6450   8096 

.7642   8832 

.8441   9264   0736 

1.1847 

50 

•20 

,6472   8111 

.7623   8821 

.8491   9289   0711 

1.1778 

40 

30 

.6494   8125 

.7604   8810 

.8541   9315   0685 

1.1708 

30 

40 

.6517   8140 

.7585   8800 

.8591   9341   0659 

1.1640 

20 

50 

.6539   8155 

.7566   8789 

.8642   9366   0634 

1.1571 

10 

41°00' 

.6561  9.8169 

-.7547  9.8778 

.8693  9.9392  0.0608 

1.1504 

49°00' 

10 

.6583   8184 

.7528   8767 

.8744   9417   0583 

1.1436 

50 

20 

.6604   8198 

.7509   8756 

.8796   9443   0557 

1.1369 

40 

30 

.6626   8213 

.7490   8745 

.8847   9468   0532 

1.1303 

30 

40 

.6648   8227 

.7470   8733 

.8899   9494   0506 

1.1237 

20 

50 

.6670   8241 

.7451   8722 

.8952   9519   0481 

1.1171 

10 

42°00' 

.6691  9.8255 

.7431  9.8711 

.9004  9.9544  0.0456 

1.1106 

48°00' 

10 

.6713   8269 

.7412   8699 

.9057   9570   0430 

1.1041 

50 

20 

.6734   8283 

.7392   8688 

.9110   9595   0405 

1.0977 

40 

30 

.6756   8297 

.7373   8676 

.9163   9621   0379 

1.0913 

30 

40 

.6777   8311 

.7353   8665 

.9217   9646   0354 

1.0850 

20 

50 

.6799   8324 

.7333   8653 

.9271   9671   0329 

1.0786 

10 

43°00' 

.6820  9.8338 

.7314  9.8641 

.9325  9.9697  0.0303 

1.0724 

47<'00' 

10 

.6841   8351 

.7294   8699 

.9380   9722   0278 

1.0661 

50 

20 

.6862   8365 

.7274   8618 

.9435   9747   0253 

1.0599 

40 

30 

.6884   8378 

.7254   8606 

.9490   9772   0228 

1.0588 

30 

40 

.6905   8391 

.7234   8594 

.9545   9798   0202 

1.0477 

20 

50 

.6926   8405 

.7214   8582 

.9601   9823   0177 

1.0416 

10 

44°00' 

.6947  9.8418 

.7193  9.8569 

.9657  9.9848  0.0152 

1.0355 

46°00' 

10 

.6967   8431 

.7173   8557 

.9713   9874   0126 

1.0295 

50 

20 

.6988   8444 

.7153   8545 

.9770   9899   0101 

1.0235 

40 

.   30 

.7009   8457 

.7133   8532 

.9827   9924   0076 

1.0176 

30 

40 

.7030   8469 

.7112   8520 

.9884   9949   0051 

1.0117 

20 

50 

.7050   8482 

.7092   8507 

.9942   9975   0025 

1.0058 

10 

45°00' 

.7071  9.8495 

.7071  9.8495 

1.0000  0.0000  0.0000 

1.0000 

45°00' 

Nat.   Log. 

Nat.   Log. 

Nat.   Log.   Log. 

Nat. 

ANGLE. 

COSINES. 

SINES. 

COTANGENTS.     TANGENTS. 

ANGLE. 

PAGES 

VII.    TRIGONOMETRIC  FUNCTIONS,  -  -  -         60-104 

A  five-place  table  of  natural  sines,  cosines,  tangents, 
and  cotangents  of  angles  0°-180°,  to  minutes,  and  a 
six-place  table  of  their  logarithms,  with  differences 
of  logarithms  for  seconds  expressed  in  units  of  the 
sixth  decimal  place. 

VIII.    NATURAL  LOGARITHMS,  .  -  -  -       105-117 

A  six-place  table  of  natural  logarithms  of  the  deci- 
mal numbers,  .01,  .02,  .03,. .9.99,  of  the  natural  num- 
bers 1,  2,  3,. .1218,  and  of  the  prime  numbers  between 
1218  and  10000, 

IX.    PRIME  AND  COMPOSITE  NUMBERS,  -  -       118-13: 

A  table  of  prime  and  composite  numbers  from  1  to 
20000,  with  the  factors  of  the  composite  numbers 
that  are  not  divisible  by  2  or  5,  and  ten-place  logar- 
ithms of  the  primes. 

X.    SQUARES, 138-139 

A  table  of  the  squares  of  the  natural  numbers 
1,  2,  3,..999. 

XI.    CUBES, 140-141 

A  table  of  the  cubes  of  the  decimal  numbers  .1,  .2, 
.3,..99.9. 

XII.    SQUARE-ROOTS, 142-145 

A  table  of  the  square-roots,  to  four  decimal  places, 
of  the  natural  numbers  1,  2,  3,. .999,  and  of  the  deci- 
mal numbers  .1,  .2,  .3,.. 99.9. 

XIII.  CUBE-ROOTS, 146-151 

A  table  of  the  cube-roots,  to  four  decimal  places,  of 
the  natural  numbers  1,  2,  3,. .999  of  the  decimals  .1,  .2, 
.3,..99.9,  and  of  the  decimals  .01,  .02,  .03,..9.99. 

XIV.  RECIPROCALS, 152-153 

A  table  of  the  reciprocals  of  the  decimal  numbers 
.01,  .02,  .03,.. 9.99. 

XV.    QUARTER-SQUARES, 154-157 

A  table  of  the  quarter-squares  of  the  natural  num- 
bers 1,  2,  3,..2000. 

XVI.    BESSEL'S  COEFFICIENTS,  ....  158 

A  table  of  BessePs  coefficients  for  second,  third, 
fourth,  and  fifth  differences,  for  interpolation. 

XVIT.    BINOMIAL  COEFFICIENTS,       -  -  -  .  159 

A  table  of  binomial  coefficients  for  second,  third, 
fourth,  and  fifth  differences,  for  interpolation. 

XVIII.    ERRORS  OF  OBSERVATION,     -  -  -  .  160 

A  table  of  ordinates  of  the  probabilitj--curve,  values 
of  probability  integrals,  and  other  values. 


/: 


Mathematical  Text-BooMl 


PRICE-LIST,  OCTOBER  i,  1896. 


I.  A  DRILL-BOOK  IN  TRIGONOMETRY. 

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